Hamilton, who won on the same circuit past year, strengthened his lead in the 2018 driver standings with 95 points, 17 points ahead of second-placed Vettel. Team mate Valtteri Bottas took second place while Red Bull's Max Verstappen took third place after a botched pit stop ruined Sebastian Vettel's chance of making podium during a virtual safety auto stint.
Lewis Hamilton believes Mercedes will be able to apply pressure to Ferrari on a more consistent basis, such was the level of his performance in the Spanish Grand Prix. This opposed to Hamilton and Bottas running on the Super Soft tyre. "But we still have improvements to make and performance to add to the vehicle". We'll race hard and try and get the 1-2 we deserved in Baku. "This is a good way to start the weekend".
For Vettel, the pitstop strategy wasn't the best as the driver was called in on Lap 40 for a second pitstop. The defending four-time world champion dominated from start to finish, save for a spell during the mid-race pit-stops, and clocked a series of record laps as he registered his second successive win.
Hamilton echoed the optimism coming from Wolff.
"I think today has been a rejuvenating experience", he said.
The safety vehicle has helped add to the drama of the early part of the 2018 season and its appearance early in Sunday's race means it has been used in the opening five races of a championship for the first time.
"Our understanding of the auto and the improvements that we're making are important too".
"I'm almost in the groove", he added.
"The team have been working very hard to understand the tyres and how the auto works, so I think it all came together this weekend".
Hawaii volcano eruption could blast fridge-sized boulders, ash into the air
The volcano , which spread lava during the week, also threatened the geothermal power plant, the Puna Geothermal Venture plant. Ige said crews at the plant near the lava outbreak accelerated the removal of stored flammable fuel with safety in mind.
Some observers were sceptical of this explanation, but Wolff said Mercedes, too, were experiencing heavier than expected tyre wear - and in fact had brought forward Hamilton's only pit stop as a result of discovering at Bottas' stop that his tyres were nearly worn out. He did not look able to threaten Hamilton however, with Mercedes optimistic that they are getting to grips wth the issue of the tyre operating window.
It lifted the champions 17 points clear of Ferrari in the constructors' championship and, after four mediocre outings this year, boosted confidence ahead of the glamorous Monaco Grand Prix in two weeks time.
"This weekend, definitely we got ourselves onto the right path and I think the team just did an exceptional job, managing all aspects and improving in all areas".
Red Bull's Max Verstappen completed the podium despite suffering front-wing damage two-thirds of the way through the race, while Ferrari's Sebastian Vettel had to settle for fourth.
Mercedes held firm to their one-stop plan.
Lap 2/66 Romain Grosjean has heavy damage and the safety vehicle is out.
Wolff sympathised with his rivals at the Scuderia.
"We couldn't make the tires last", said Vettel. "Ferrari did the opposite". After that I was really surprised they didn't have the pace to keep up with me.